Abracon Corporation

Quartz Crystal Application Notes

Definition of Terms

Nominal frequency: The specified center frequency of the crystal. Unit of frequency is Hertz (Hz). Quartz crystals are specified in kHz or MHz.

Crystal equivalent circuit: The crystal equivalent circuit of the quartz crystal consists of a motional capacitance Cl, the motional inductance L1, a series resistance R1, and a shunt capacitance C0. The first three parameters are known as the "motional parameters". See figure 1.

Fig. 1

Operating mode: The quartz crystal could operate at its Fundamental mode or harmonic modes. The fundamental mode is always the preferred oscillating mode. Odd harmonics such as 3rd, 5th, 7th, etc. are overtone modes.

Frequency stability: The maximum allowable frequency deviation from the ambient temperature over the temperature range. Frequency stability is expressed in percent (%) or parts per millions (ppm). The frequency stability is determined by cut type, angle cut, angle cut tolerance, mode of operation, package styles, and mechanical
dimensions of the quartz blank.

Series vs. Parallel resonance: When a crystal is operating at series resonance (Fs), it looks resistive in the circuit. At this point \XL\ = \XC\. In series resonance, load capacitance does not have to be specified. The antiresonant frequency (Fa) occurs when the reactance in the series branch is equal to CO.When a crystal is operating at parallel resonance, it looks inductive in the circuit. The crystal equivalent circuit can be simplified as a series
resistance Re with a reactance Xe.The difference in frequency between the Fs and Fa depends on the
CO/C1 ratio of the crystal unit, and the inductance LI. In parallel resonance, the load capacitance shall be specified.

Fig. 2

Equivalent Series Resistance (ESR): The value of impedance the crystal exhibits in the operating resonant circuit.

Aging: The relative frequency change over a certain period of time and is typically expressed as a maximum value in parts per million per year (ppm/year). Typically, aging is computed within the first 30 days to 90 days and predicted exponentially over a longer period usually a year.

Operating temperature: The minimum and maximum temperatures within which crystal unit operates under specified conditions.

Storage temperature: The minimum and maximum temperatures that the crystal unit can be safely stored.
Drive level: A function of the driving or excitation current flowing through the crystal. The drive level is the amount of power dissipated in the crystal and is expressed in milliwatts or microwatts. Drive level should be
kept at a safe minimum condition to assure proper start-up. Excessive drive level will result in possible long-term frequency drift or crystal fracture.

Load capacitance: Load capacitance (CL) is the amount of capacitance that the oscillator exhibits when looking into the circuit through the two crystal terminals. Load capacitance needs to be specified when the crystal is used in a parallel mode. Load capacitance is calculated as follows:

Pierce circuit

ColpittsFig. 5

CL=

(C1 x C2)(C1 + C2)

+ Cstray

Spurious responses: Unwanted resonance usually above the operating mode, specified in dB max. or number of times of main mode ESR value. Frequency range is specified within couple of hundreds kilohertz.

Fig. 6

Quartz Crystal Glossary of Terms

Crystal cuts: A blank wafer is obtained by cutting the quartz bar at specific angles to the various axes. The choice of axis and angle cut determines the physical and electrical parameters of
the resonator. Figure 7 shows combinations of X, Y, and Z rotational cuts which are labeled in industry as AT, BT, CT, DT cut, etc. The most two common cuts in Abracon crystals are AT and BT-cuts. There are differences in temperature coefficients of the two cuts.

Fig. 7

Vibration modes: The crystal vibrates and produces a steady signal when it is excited with a voltage. The mode of vibration depends on crystal cuts such as thickness shear for AT and BT cuts, length-width flexure for tuning fork, Face shear for CT, DT cuts, etc. Figure 8 shows a thickness-shear mode.

Fundamental

Third-Overtone

Fifth-Overtone

Fig. 8

Shunt capacitance CO: The static capacitance between the electrodes (Ce) together with holder capacitance (Ch).

Co = Ce+Ch

Ch varies between 0.6pF to 0.8pF depending on mounting method.

Motional capacitance C1: The capacitance of the nominal arm of the equivalent circuit. C1 results from the elasticity of the quartz blank.

C1 (pF) = 0.22 x A (m") x F (Hz) / 1670

Where A = area of electrode in m2

Quality factor Q: The factor that represents the sharpness of the resonant curve. Quartz crystal has a very high Q compared to other resonators typically in 10,000 to 100,000s.

Pullability: When a crystal is operating at parallel resonance, it looks inductive in the circuit. As the reactance changes, the frequency changes correspondingly, thus change the pullability of the crystal. The difference in frequency between the Fs and Fa depends on the CO/CI ratio of the crystal unit and the load capacitance CL.

Delta F from series resonant to parallel resonant in ppm:

Pullability can be expressed in terms of load sensitivity (TS) in ppm/pF.

Negative resistance (-R): Negative resistance is used to evaluate circuit oscillation allowance. Lack of negative resistance could lead to initial circuit start-up and and unstable oscillation
at steady state.

Study the Voltage Gain from output to input Vi/Vo= C2/C1.
It is very common to select equal values of C1 and C2 in the circuit, but sometimes it is necessary to make the output load capacitance (C2) higher to compensate for the signal losses through the crystal and feed back loop.

Inductorless Third (3rd) Overtone: The Inductorless 3rd-0vertone circuit is similar to the fundamental frequency circuit except the feedback resistor value is made much smaller (typical value varies between 2 kQ to 6 kQ). In this case, the component of inductive admittance due to the resistor is greater than the admittance of the loading
capacitance at the fundamental frequency, thereby preventing oscillation at the fundamental frequency. In the meantime, the inductive admittance at the overtone is less than the admittance of the Load Capacitor thus enabling the oscillation at the third-overtone. (See fig 1.)

U1: ASCIY1: CrystalC1 C2: Load Capacitance

Fig. 1

Tuning Tank LC Overtone Circuit.

In an overtone mode, an additional inductor LI and capacitance CC is required to select the Srd-Overtone mode, while suppressing or rejecting the fundamental mode. Choose LC and CC component values in the Srd-overtone crystal circuit to satisfy the following conditions:

The LC / CC component form a series resonant circuit at a frequency below the fundamental frequency, which makes the circuit look inductive at the fundamental frequency. This condition does not favor to oscillation at the fundamental mode.

The LI / CC and C2 components form a parallel resonant circuit at a frequency about half-way between the fundamental and Srd-Overtone frequency. This condition makes the circuit capacitive at the 3rd-Overtone frequency, which favors the oscillation at the desired Overtone mode.
(See figure 2).

The Lc tank may be located at either input or output of the inverter. However, the Lc tank at the out put is referred, because it helps to clean up all unwanted modes before signal goes through the crystal.

CONTROL UNWANTED MODES IN CRYSTALS:

Unwanted modes are resonant modes in addition to the desired modes (Fundamental, Third-Overtone, Fifth overtone, etc.). The frequencies of these unwanted modes are usually slightly higher than the desired modes within couple of hundreds kilohertz. In oscillator applications, it is necessary to control unwanted modes
as lower as possible to prevent circuit oscillating in the "spurious mode". See Figure 3. The design of large electrodes on crystal to produce large pulling is a common cause of promoting spurs. Unwanted modes are usually specified in terms of resistance or in terms of the ratio of resistance of the unwanted mode to the resistance of the main mode over a bandwidth of desired frequency. A resistance ratio of 2:1 or a minimum of 3dB separation is usually adequate.

Fig. 3

Questions & Answers

Q: Why does my crystal works sometimes, but not others?

A: This is the most common complaint heard from crystal users. Unless the crystal supplier knows this common mode of failure, and applies preventive measures, this common problem can be solved earlier in design stage. Some customers describe these crystals as "sleeping crystals". The circuit start-up sometimes and does not at other times, unless been touched with a scope probe or fingers. Abracon predicts this problem in our Design and
Process Failure Mode Effect Analysis (DFMEAand PFMEA) with two main root causes:

Blank cleanliness.

Drive level dependency.

IC matching.

Blank cleanliness: We use special blank wafer ultrasonic cleaning procedure in De-ionized water and 99.99% Isopropyl Alcohol with modulated air method to guarantee highest quality.

Drive level dependency: On most production lots, we perform 100% DLD tests at five levels minimum starting from 1 pW to 500pW. The DLD test will guarantee that the changes in ESR and frequency are within maximum limits thus assure the initial power start-up.

A: Many applications in VCXO, PLL network require a crystal with pulling characteristics. The pullability of the crystal can be explained as follow:
When a crystal is operating at parallel resonance, it looks inductive in the circuit. As the reactance changes, the
frequency changes correspondingly, thus change the pullability of the crystal. The difference between the Fs and Fa depends on the ratio CO/C1 ratio of the crystal.

The following crystal parameters specify the pullability:

Motional capacitance C1 in fF.

Motional inductance LI in mH

The difference of the parallel resonant frequency

F = FL2 - FL1

Ratio of shunt capacitance to motional capacitance CO/C1. The smaller ratio the better the pulling. The pullability of the crystal can be designed to meet customer's requirements. However, the pulling function varies with package size, electrode size, frequency, load capacitance range, and operating mode. Please contact Abracon whenever you have a need for a pulling crystal.

Q: What is the trend of crystal packaging and advantages?

A:

Minimizing the size and weight of mobile communication application such as cellular phones, PCMCIA, PDA, etc.

Advanced small quartz blank design in smaller ceramic packages such as 5.0 x 3.2mm, 3.2 x 2.5mm, etc. The
fundamental frequency increases up to 66MHz helps simplify circuit design and is more efficient compared to the
old traditional third-overtone circuit complexity.

Features of E-Beam sealing:

Tight stability and tight tolerance (+10ppm).

Low ESR and high reliability by vacuum package.

Resistance to shock and moisture.

High productivity captured with seam sealing method.

Miniaturization by fine processing of E-Beam.

LTCC packaging helps reducing size and external components.

Q: Introduction to Abracon Programmable Oscillators:

A: Abracon offers quick-turn programmable oscillators in four different package styles; the ceramic package 7.0x5.0x1.6 mm, plastic molded package similar to Epson SG-8002, and the 14 pin and 8 pin dip packages. The single PLL architecture with EPROM programmable generates a custom frequency derived from an internal
crystal between lOMHz to 25MHz. The main advantages of the programmable oscillators are:

A: A PLL allows a frequency to be generated from any other frequency, where:

CLK OUT =

REF. CLK * P/QPost-Divider

Q: What is jitter?

A: Jitter is the uncertainty or short-term variations of a digital waveform timing from their ideal positions in time.
The waveform transition could be too early or too late compared to the ideal waveform timing.

Q: How to measure jitter?

A: We use LeCroy digitizing oscilloscope with jitter timing software for jitter measurement and analysis. The scope must have the bandwidth at least five times the frequency of the waveform since the waveform jitter is measured as each rising cycle crosses the threshold voltage. The larger number of continuous cycles the more
accurate is the jitter distribution. Jitter is measured in cycle-to-cycle (or absolute jitter) or one sigma jitter (rms.) using the histogram analysis. Unit of jitter is ps.

Q: Can phase noise be improved in designs?

A: Yes. Crystal oscillators can be designed to minimize their phase noise characteristics. Special applications such as wireless require best phase noise both at far-end and close-end. Crystal parameters and mounting methods directly affect close-end phase noise 300Hz offset from carrier. The oscillator front-end and output buffer primarily control phase noise with offset frequency from carrier greater or equal to 1kHz.

Q: Why the Overall frequency stability is specified in crystal oscillators but not in crystals?

A: The crystal oscillator is typically used as a master clock for the microprocessor and its parameters are not affected by the internal characteristics of the microprocessor such as variation in load capacitance and other variables that could affect the change in frequency at room and over temperature. The over all frequency stability in crystal oscillators is typically +100ppm max. and includes frequency calibration at 25°C, over temperature, frequency changes due to load, supply, aging, vibration, and shock.

Q: What is the start-up time?

A: Start-up time is the delay time between the oscillation starts from noise until it reaches its full output
amplitude when power is applied. The supply voltage must be applied with a defined rate or rise. The start-up time
varies from microseconds to milliseconds depending on frequency, ASIC speed and logic. Please see figure 1.

Figure 1

Q: What is Tristate Enable/Disable mode?

A: When the voltage at the control pin is set to a logic low "0",the out put is in Tri-state mode that is High Impedance. The disabled current is usually lower than its normal operating current but not completely cut-off as it was seen in the Stand-by mode, where the oscillation is shut down completely.There is an internal pull-up resistor between control pin and supply (typically 1ook Ohms), therefore the control pin can be left open (floating) if unused.

Q: What is jitter and how to specify its maximum value?

A: Jitter is noise caused by many sources in crystal oscillators.
Major sources of noise are:

Power supply noise.

Integer multiples of the signal source frequency (harmonics).

Load and termination conditions.

Amplifier noise.

Circuit configuration (PLLs, Multiplier, Overtone, etc.)

The following methods can be used to suppress the noise conditions in the above sources:

Make sure that the power supply noise is filtered by using by pass capacitors, chip beads, or RC filters.

If jitter is critical in some applications, especially for high- fre quencies noise, use low harmonics outputs or sine output.

Make sure that load and termination conditions are optimized to avoid reflected power back to its output.

Typically, PLLs, Multiplier or Programmable designs produce higher jitter than the conventional fundamental design.
It is very important to understand the jitter requirements from the
application to specify the right specification for crystal
oscillators.

We can classify two types of jitters:

Cycle to cycle jitter

Period jitter.

CYCLE TO CYCLE JITTER

The Cycle to cycle jitter is the maximum difference in time between several measured periods. Usually a minimum of ten (10) cycles is used where T1 to T10 were recorded . See fig. 2.

Figure 2

PERIOD JITTER.

The period jitter is the maximum change of a clock edge. It is usually expressed as peak-to-peak jitter and can be converted to rms value by multiplying to (0.5) x (0.707). The period jitter can only be measured at each cycle but not multiple cycles. See figure 3.
Typical jitter recorded in Abracon oscillators varies from 20ps to 60ps rms.

Figure 3

Q: What is phase noise and how to measure it?

A: Phase noise is the expression of noise in the frequency domain. It is a measure of the short-term frequency fluctuations of the oscillator. It is usually specified as the single sideband power density in a 1 Hz bandwidth at a specified offset frequency from the carrier.
In order to measure phase noise, it is necessary to pair a similar device-under-test with one unit set a VCXO and other set a fixed XO. Please see block diagram in figure 4.

Figure 4

Typical phase noise in Abracon VCXO and oscillators:

OffsetFrequency(Hz)

PhaseNoise(dBc/Hz)

10

-70

100

-110

1,000

-125

10,000

-150

100,000

-160

CMOS RISE AND FALL TIMES

The rise and fall time on the CMOS technology depends on its speed (CMOS, HCMOS, ACMOS, BICMOS), the supply voltage, the load capacitance, and the load configuration. Typical rise and fall time for CMOS 4000 series is 30ns, HCMOS is 6ns, and for ACMOS (HCMOS, TTL compatible) is 3 ns max.

Typical rise and fall time is measured between 10% to 90% of its waveform level.

Output WaveformFigure 1

ACMOS OUTPUT TERMINATION TECHNIQUES

Due to the fast transition time of the ACMOS (HCMOS/TTL compatible) device, proper termination techniques must be used when testing or measuring electrical performance characteristics.
Termination is usually used to solve the problem of voltage prreflection, which essential cause steps in clock waveforms as well as overshoot and undershoot. Such effect could result in false clocking of data, as well as higher EMI and system noise.

Figure 2

Termination is required also because of the length of the trace on the PC board and its load configuration.
There are three general methods of terminating a clock trace, which is a process of matching the output impedance of the device with the line impedance:

Series termination;

Pull-up/Pull-down termination;

Parallel-AC termination

METHOD 1:

Series termination (Fig. 3)Figure 3Rs > ZT - Ro

In series termination, a damping resistor is placed close to the source of the clock signal. Value of Rs must satisfy the following requirement:

METHOD 2:

Pull-Up / Pull-Down Resistors (Fig. 4)Figure 4

In pull-up/pull-down termination, the Thevenin's equivalent of the combination is equal to the characteristics impedance of the trace. This is probably the cleanest, and results in no reflections, as well as EMI.

RT ~ ZT

METHOD 3:

Parallel AC Termination (Fig. 5)Figure 5

In parallel AC termination, a R-C combination is placed at the load. The value of the capacitor must be chosen carefully, usually smaller than the 50pF. This termination is not recommended because it will degrade the rise and fall time of the clock, although it draws no DC current.